State an expression for the solubility product constant, \({K_{{\text{sp}}}}\), for copper(II) hydroxide.

The solubility product of copper(II) hydroxide is \(4.8 \times {10^{ - 20}}\) at a given temperature.

Determine the concentration, in \({\text{mol}}\,{\text{d}}{{\text{m}}^{ - 3}}\), of \({\text{C}}{{\text{u}}^{2 + }}{\text{(aq)}}\) in the solution when copper(II) hydroxide is precipitated.

\({\text{(}}{K_{sp}} = {\text{) [C}}{{\text{u}}^{2 + }}{\text{(aq)][O}}{{\text{H}}^ - }{\text{(aq)}}{{\text{]}}^2}\);

Ignore state symbols.

\(4.8 \times {10^{ - 20}} = 4{x^3}\);

\((x = ){\text{ [C}}{{\text{u}}^{2 + }}{\text{(aq)]}} = 2.3 \times {10^{ - 7}}{\text{ (mol}}\,{\text{d}}{{\text{m}}^{ - 3}}{\text{)}}\);

Award [2] for final correct answer.

If (b) is attempted any solution should be accepted where the product of the concentrations of Cu²⁺(aq) and OH^–(aq) matches the \({K_{sp}}\) value OR if stated that one value unknown, award [2], only if (a) has been answered.

There were two G2 comments on this question stating essentially based on the wording of the stem of the question a precise value of the concentration of copper(II) ions can only be deduced if the concentration of hydroxide ions is in addition known. The comments made are valid. This was discussed at length during standardization and grade award and several scripts were examined to see how candidates handled this question. Nearly every candidate who managed to get the \({K_{{\text{sp}}}}\) expression correct in (a) took this to read as a saturated solution and calculated \({\text{[C}}{{\text{u}}^{2 + }}{\text{(aq)]}} = 2.3 \times {10^{ - 7}}{\text{ mol}}\,{\text{d}}{{\text{m}}^{ - 3}}\), which was the original intention of the MS. However, the MS took into account a number of possibilities here – for example if (b) was attempted any solution was accepted where the product of the concentrations of \({\text{C}}{{\text{u}}^{2 + }}{\text{(aq)}}\) and \({\text{O}}{{\text{H}}^ - }{\text{(aq)}}\) matched the \({K_{{\text{sp}}}}\) value or if it was stated that one value was unknown, as long as candidate got an answer in (a). Hence candidates were not penalized in any way in the marking of this question as all candidates getting a \({K_{{\text{sp}}}}\) expression did actually score in (b) in a way or another. Overall the problem was typically more one of candidates not even getting started on the \({K_{{\text{sp}}}}\) expression in part (a) and all sorts of strange, totally incorrect \({K_{{\text{sp}}}}\) expressions were suggested (e.g. using water instead of hydroxide).

There were two G2 comments on this question stating essentially based on the wording of the stem of the question a precise value of the concentration of copper(II) ions can only be deduced if the concentration of hydroxide ions is in addition known. The comments made are valid. This was discussed at length during standardization and grade award and several scripts were examined to see how candidates handled this question. Nearly every candidate who managed to get the \({K_{{\text{sp}}}}\) expression correct in (a) took this to read as a saturated solution and calculated \({\text{[C}}{{\text{u}}^{2 + }}{\text{(aq)]}} = 2.3 \times {10^{ - 7}}{\text{ mol}}\,{\text{d}}{{\text{m}}^{ - 3}}\), which was the original intention of the MS. However, the MS took into account a number of possibilities here – for example if (b) was attempted any solution was accepted where the product of the concentrations of \({\text{C}}{{\text{u}}^{2 + }}{\text{(aq)}}\) and \({\text{O}}{{\text{H}}^ - }{\text{(aq)}}\) matched the \({K_{{\text{sp}}}}\) value or if it was stated that one value was unknown, as long as candidate got an answer in (a). Hence candidates were not penalized in any way in the marking of this question as all candidates getting a \({K_{{\text{sp}}}}\) expression did actually score in (b) in a way or another. Overall the problem was typically more one of candidates not even getting started on the \({K_{{\text{sp}}}}\) expression in part (a) and all sorts of strange, totally incorrect \({K_{{\text{sp}}}}\) expressions were suggested (e.g. using water instead of hydroxide).